Question(1 point) Given that $f(x)=|x|$ and $g(x)=7 x+2$, calculate (a) $(f \circ g)(x)=$ $\square$ (b) $(g \circ f)(x)=$ $\square$ (c) $(g \circ g)(x)=$ $\square$

Studdy Solution
Substitute into $g(x) = 7x + 2$:
$$g(7x + 2) = 7(7x + 2) + 2$$
Simplify:
$$= 49x + 14 + 2$$ $$= 49x + 16$$
Thus,
$$(g \circ g)(x) = 49x + 16$$
The solutions are: (a) $(f \circ g)(x) = |7x + 2|$ (b) $(g \circ f)(x) = 7|x| + 2$ (c) $(g \circ g)(x) = 49x + 16$